By the definition of the acceleration vector,
when, as time evolves,
there is a change in the velocity-vector [either in magnitude, in direction, or in both],
then there is a nonzero acceleration-vector.

You can also think about it in terms of Newton's 1st law - without forces (which means accelerations, by the 2nd law, i.e. F=ma) things move in straight lines (or not at all). Therefore, if you're changing your direction of motion, you must be under the influence of a net force and therefore accelerating.

If you doubt this, consider the reaction to acceleration: you get thrown back in the opposite direction. So, if you accelerate forward in a car, you get thrown back against the seat, but if you take a sudden turn without changing speed, you get thrown to the side. Both cases are responses to acceleration.